How to cast/teleport a ray in a material for a squinching illusion?
In the past I've succesfully done this with multiple render passes, where I first render the scene from the position of the audience, and then project it onto the screen, to then capture that from whatever angle I need.

This technique seems to be the most viable to me. If you want to project what the audience is seeing onto the surface, this approach does exactly that - and the simplest solution is often the best.

This technique however loses a lot of quality as some parts end up being more stretched then others.

You can increase the resolution until it satisfies your needs. Yes, you might &quot;waste&quot; some pixels, but that doesn't seem like a critical issue.

A way to somehow &quot;teleport&quot; the ray back. But it looks like I can only influence its direction.

Yeah, I don't think Cycles is designed for custom ray transformations such as the one you describe. This is likely not a common use case, and there is a flexibility-performance trade-off when designing renderers.
Edit: alternative suggestion
Since you have already gotten the projection to work for objects behind the &quot;screen&quot;, I can suggest scaling the screen down towards the audience - so that everything, including the cube, is behind the screen. Then you would also need to adjust the camera, and the projection would appear as you intend.

If you need to render the rest of the scene as well, you could combine that render with the rest of the scene during compositing.